Effect of reciprocity-breaking on fine-track tip/tilt systems

We analyze here a candidate system for correcting the wander of a self-channeled laser pulse using a fast-steering mirror along with a cooperative beacon imaged with a telescope. For our model system, the imaging telescope is coaxial with the propagation of the outgoing pulse. In the ideal case, any incoming light gathered from the beacon would be collimated, such that taking a centroid beacon image would yield the precise tip and tilt required for the self-channeled pulse to propagate back to the beacon on the reciprocal path. The degree to which reality differs from this ideal case determines the effectiveness of the wander correction. We simulate our system for a range of propagation and imaging conditions. We also show that in the absence of image noise (i.e., when the beacon power is arbitrarily high, and the signal-to-noise ratio is not an important consideration), the system exhibits its best performance when the receiving aperture diameter of the imaging system is close to the transverse size of the outgoing pulse, maximizing reciprocity. When realistic noise and finite beacon power are included in the simulation, however, we find that this reciprocity advantage may not be sufficient to compensate for the reduced photon count and resolving power of a small receiving aperture. In this case, the optimal aperture diameter will be the smallest possible, which allows for an acceptable signal-to-noise ratio.